Abstract

In the measurement system of interference fringe, the nonorthogonality error is a main error source that influences the precision and accuracy of the measurement system. The detection and elimination of the error has been an important target. A novel method that only uses the cross-zero detection and the counting is proposed to detect and eliminate the nonorthogonality error in real time. This method can be simply realized by means of the digital logic device, because it does not invoke trigonometric functions and inverse trigonometric functions. And it can be widely used in the bidirectional subdivision systems of a Moiré fringe and other optical instruments.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  4. J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
    [CrossRef]
  5. G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
    [CrossRef]
  6. F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
    [CrossRef]
  7. H. Hu, X. Qiu, J. Wang, A. Ju, and Y. Zhang, “Subdivision and direction recognition of λ/16 for nanometric measurement of orthogonal fringes,” Appl. Opt. 48, 6479–6484 (2009).
    [CrossRef] [PubMed]

2009 (2)

F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
[CrossRef]

H. Hu, X. Qiu, J. Wang, A. Ju, and Y. Zhang, “Subdivision and direction recognition of λ/16 for nanometric measurement of orthogonal fringes,” Appl. Opt. 48, 6479–6484 (2009).
[CrossRef] [PubMed]

2004 (1)

2001 (1)

T. B. Eom, J. Y. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

2000 (1)

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

1994 (1)

G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
[CrossRef]

1981 (1)

Berger, J.

Cheng, F.

F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
[CrossRef]

Dzieciuch, M. A.

Eom, T. B.

T. B. Eom, J. Y. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Fan, G. Z.

F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
[CrossRef]

Fei, Y. T.

F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
[CrossRef]

Heydemann, P. L. M.

Hu, H.

Jeong, K.

T. B. Eom, J. Y. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Ju, A.

Kim, J. Y.

T. B. Eom, J. Y. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Kim, K. C.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Kim, S. H.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Li, Z.

G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
[CrossRef]

Parker, R. L.

Qiu, X.

Song, J. H.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Wang, C. H.

G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
[CrossRef]

Wang, J.

Zhang, G. X.

G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
[CrossRef]

Zhang, Y.

Zumberge, M. A.

Appl. Opt. (3)

CIRP Ann. (1)

G. X. Zhang, C. H. Wang, and Z. Li, “Improving the accuracy of angle measurement system with optical grating,” CIRP Ann. 43, 457–460 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

T. B. Eom, J. Y. Kim, and K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Proc. SPIE (1)

F. Cheng, Y. T. Fei, and G. Z. Fan, “New method on real-time signal correction and subdivision for grating-based nanometrology,” Proc. SPIE 7284, 728403 (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Subintervals of nonorthogonal signals in λ / 8 subdivision.

Fig. 2
Fig. 2

Experiment system for testing the proposed method.

Tables (5)

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Table 1 λ / 8 Bidirectional Counting Principle

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Table 2 Interval Length of Eight Subintervals

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Table 3 Nonorthogonality Error Detection

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Table 4 Calculated Forward Movement Distance

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Table 5 Calculated Backward Movement Distance

Equations (13)

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{ u 1 f = U 0 sin θ u 2 f = U 0 cos θ .
{ u 1 b = U 0 sin θ u 2 b = U 0 cos θ ,
{ r 11 = u 1 + u 2 r 12 = u 1 u 2 .
{ u 1 = U 0 sin θ u 2 f = U 0 sin ( θ + π 2 + Δ φ ) ,
{ u 1 = U 0 sin θ u 2 b = U 0 sin ( θ π 2 Δ φ ) .
L = N d + θ 2 π d , θ [ 0 , 2 π ) ,
L = N 8 d 8 + 4 θ π d , θ [ 0 , π 4 ) ,
N = N 8 8 .
Δ φ = 1 2 C h p C e C h p π .
Δ φ = C e b 1 2 C h p C h p π .
L = N d + n C p d , n ( C p , C p ) ,
L = N 8 d 8 + n C p d , n ( C p 8 , C p 8 ) ,
L = ( π 2 Δ φ 8 π N 8 a + π + 2 Δ φ 8 π N 8 b ) d + n C p d ,

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